EPA has recently proposed Maximum Achievable Control Technology (MACT) limits for HAPs emitted by coal-fired electric utility generating units (2011). In this paper, we first evaluate the statistical assumptions that EPA’s rulemaking is based upon. When the normality assumption is violated as actual emission data suggest, we propose parametric and non-parametric methods to construct UPLs for the arithmetic mean of emission samples. We derive an approximate distribution of the arithmetic mean of log-normally distributed emission samples based on Fenton’s approximation (Fenton 1960). We use simulations to illustrate that the approximate distribution achieves desired confidence level that comparable with the exact distribution and other approximate distributions (Barakat 1976, Bhaumik and Gibbons 2004). When the sample independency is violated for continuous emission data, we construct the UPL based on the log-normal approximation when temporal correlation of emission data is incorporated. Moreover, we apply the bootstrap method to examine the distribution of UPLs and compare the UPL estimated from non-parametric method with various parametric methods through simulation studies. Finally, we test our approaches using actual stack test data and two-year continuous emission data from five top-performing coal-fired utility plants.